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A088701 Smallest semiprime such that n primes will follow until the next semiprime.

%I A088701 #23 Aug 18 2018 08:44:38
%S A088701 9,4,10,95,818,2681,16053,35981,797542,1069541,340894,6974465,3586843,
%T A088701 2070050198,5238280946,14499777101,2601693504238,7472089131123
%N A088701 Smallest semiprime such that n primes will follow until the next semiprime.
%C A088701 Is this sequence infinite? - _David A. Corneth_, Aug 17 2018
%F A088701 A088700(a(n)) = n and A088700(k) <> n for 1 <= k < a(n).
%t A088701 om = Array[PrimeOmega, 1100000]; sp = Flatten@ Position[om, 2]; Table[ sp[[ SelectFirst[ Range[Length[sp] - 1], Count[Take[om, {sp[[#]], sp[[# + 1]]}], x_ /; x == 1] == j &, 0]]], {j, 0, 10}] (* _Giovanni Resta_, Aug 16 2018 *)
%o A088701 (Perl) use ntheory ":all";
%o A088701 my($l,$nextn,@C)=(4,0);
%o A088701 forcomposites {
%o A088701   if (is_semiprime($_)) {
%o A088701     my $c = prime_count($l+1,$_-1);
%o A088701     if (!defined $C[$c]) {
%o A088701       $C[$c] = $l;
%o A088701       while (defined $C[$nextn]) { print "$nextn $C[$nextn]\n"; $nextn++; }
%o A088701     }
%o A088701     $l = $_;
%o A088701   }
%o A088701 } 5,1e7;  # _Dana Jacobsen_, Aug 16 2018
%Y A088701 Cf. A214520 (primes that are the only prime between consecutive semiprimes).
%K A088701 nonn,more
%O A088701 0,1
%A A088701 _Reinhard Zumkeller_, Oct 08 2003
%E A088701 a(11)-a(15) from _Donovan Johnson_, Mar 14 2010
%E A088701 a(16) from _Giovanni Resta_, Aug 17 2018
%E A088701 a(17) from _Giovanni Resta_, Aug 18 2018